Question

write a true conditional that has a false converse. choose the correct answer below. a. if a triangle has all sides equal, then it is an equilateral triangle. b. if a shape is a square, then it is a four - sided polygon. c. if two sides of a triangle are equal, then it is an equilateral triangle. d. if two angles of a triangle are equal, then two sides of the triangle are equal.

Explanation:

A conditional statement "if p then q" has a converse "if q then p". For a triangle, if two angles are equal, then the two sides opposite those angles are equal (the Isosceles - Triangle Theorem). The converse here is a well - known and true geometric property. In option A, the converse of an equilateral triangle definition is incorrect as just having equal sides doesn't necessarily mean it's an equilateral triangle in all contexts of the converse statement logic. In option B, a four - sided polygon being a square if it's a square is a tautology and not a proper converse in the conditional - statement sense. In option C, the converse about two sides of a triangle being equal and it being equilateral is incorrect as two equal sides make it isosceles, not equilateral.

Answer:

D. If two angles of a triangle are equal, then two sides of the triangle are equal.